Optics Question 100
Question: A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm. Then the refractive index of its material will be
[BHU 1997; UPSEAT 1995]
Options:
A) 3.0
B) 2.0
C) 2.5
D) 1.5
Show Answer
Answer:
Correct Answer: D
Solution:
Here $ \frac{1}{F}=\frac{2}{f}+\frac{1}{f _{m}} $ Plano-convex lens silvered on plane side has $ f _{m}=\infty $ .
$ \therefore $ $ \frac{1}{F}=\frac{2}{f}+\frac{1}{\infty }\Rightarrow \frac{1}{30}=\frac{2}{f}\Rightarrow f=60cm $ Plano-convex lens silvered on convex side has $ f _{m}=\frac{R}{2} $
$ \therefore $ $ \frac{1}{F}=\frac{2}{f}+\frac{2}{R}\Rightarrow \frac{1}{10}=\frac{2}{60}+\frac{2}{R}\Rightarrow R=30cm $ Now using $ \frac{1}{f}=(\mu -1)( \frac{1}{R} ) $ , we get $ \mu =1.5 $
